This report describes the four ACT-R models and the learning outcomes produced by the changes in paramters. The report also describes how these models fit behavioral data and details the properties of the best fitting models and parameters. The specific objectives of this project is to test if the RLWM task can be modeled well by a group of pure and combined declarative learning models. After fitting the models to participant data we aim to extract parameters that may explain why and how learning resulted as obsereved. If the parameters describe individual differences in learning would the parameters predict other behavioral data like working memory capacity?
Below are the 4 ACT-R models tested. Note that the bolded names appear through-out this document.
RL: Pure RL model based on learning of production utility in ACT-R. learning rate (alpha) and softmax temperature are the only 2 parameters
LTM: A declarative model that solely depends on starage and retirieval of stimuli, response and outcome in ACT-R’s declarative memory. This model depends on decay rate, retrieval noise and
meta_RL: This is a combined RL - LTM model. Information about trials performed by the RL system is shared and stored in LTM (declarative) for use. An isolated (meta) RL system (a set of productions) learns and determines which sub-system, RL or LTM, is used throughout learning. Which subsystem is preferred depends on the specific set of parameters.
biased: This is a combined RL-LTM model. Information about trials performed by the RL system is not shared with the LTM subsystem. An additional “strategy” parameters specifies a bias towards the RL model at the 20, 40, 60, and 80 percent of learning and test trials.
Talk about BIC and the model fitting
The LTM model fits the most number of participants (54) followed by the biased version of the combined RL-LTM model (18) and the meta-RL combined model at third (10). The RL only model has only one participant that fit it best.
Figure 1.
There is only 1 RL best fitting model. For the most popular model, LTM, that fit (54) participants, there are only 13 best fitting parameter sets. The biased model seems to be the most diverse at 17 parameter sets for (18) participants. The meta-RL model closely follows the biased model interms of diversity of parameter sets at 8 parameter sets for (10) subjects.
The following two boxplots (figures 2 and 3) show the medians and ranges of the BIC values that determined that the LTM model is the best fitting model. Boxplot 1 shows the range in BIC across all participants whether they fit that model best or not and therefore has equal number of data points (83). The second boxplot however displays BIC medians and ranges for only the best fitting participants for that data (that is why the plot for RL is a line representing the only data point).
Figure 2.
This second boxplot was in an effort determine how well a model type fits its preferred set of behavioral data. This might be redundant. The LTM model fits data much better than the other group (This might need a statistical test).
Figure 3.
Looking at the learning curves for the four models in Figure 4, the differences in learning rates are apparent as are other features like the separation between the two set sizes. In the plot below each data point is the average accuracy, for that number of stimulus presentations, across all parameter combinations. The LTM and RL models predict that an increase in set-size does not diminish learning rate and accuracy. But this analysis washes out the individual differences that could be captured by the diverse set of parameter combinations.
Figure 4.
Figure 5.
There are five outcome measures of interest in the RLWM task: accuracy at the end learning, accuracy at test, learning rate characterized as number of stimulus presentations to reach 95% accuracy, the differences in learning of set3 and set 6 and also the level of preserved learning at test for both set-sizes. The following analysis compares the model data with behavioral data.
#> subjects model learnDiff
#> 1 6200 biased -1.041667e-01
#> 2 6201 LTM -5.208333e-02
#> 3 6202 biased -1.446759e-01
#> 4 6204 LTM -1.250000e-01
#> 5 6205 LTM -1.250000e-01
#> 6 6206 biased -4.861111e-02
#> 7 6207 LTM -5.439815e-02
#> 8 6209 biased -9.837963e-02
#> 9 6210 LTM 1.041667e-02
#> 10 6211 LTM 6.712963e-02
#> 11 6213 biased -1.250000e-01
#> 12 6214 biased -2.465278e-01
#> 13 6215 LTM -3.472222e-03
#> 14 6216 LTM -3.472222e-02
#> 15 6217 LTM -1.851852e-02
#> 16 6218 biased -2.337963e-01
#> 17 6219 LTM -3.472222e-02
#> 18 6220 LTM -2.662037e-02
#> 19 6223 meta -1.967593e-02
#> 20 6225 LTM -8.564815e-02
#> 21 6226 LTM -1.307870e-01
#> 22 6230 biased -1.180556e-01
#> 23 6231 LTM 4.629630e-02
#> 24 6234 LTM -1.122685e-01
#> 25 6235 biased -2.349537e-01
#> 26 6238 LTM -6.365741e-02
#> 27 6241 meta -7.407407e-02
#> 28 6242 meta -5.787037e-03
#> 29 6244 biased -2.233796e-01
#> 30 6245 LTM -7.060185e-02
#> 31 6246 LTM 3.009259e-02
#> 32 6247 biased -3.101852e-01
#> 33 6250 LTM -5.902778e-02
#> 34 6253 LTM -5.902778e-02
#> 35 6256 LTM -7.291667e-02
#> 36 15000 LTM -9.259259e-02
#> 37 15001 LTM -5.787037e-03
#> 38 15002 biased -2.256944e-01
#> 39 15003 LTM -7.638889e-02
#> 40 15004 meta -5.555556e-02
#> 41 15005 biased -2.557870e-01
#> 42 15006 LTM -1.412037e-01
#> 43 15007 LTM -1.342593e-01
#> 44 15008 LTM -7.291667e-02
#> 45 15009 meta 2.314815e-02
#> 46 15010 LTM -3.587963e-02
#> 47 15011 LTM 4.513889e-02
#> 48 15012 LTM -2.314815e-02
#> 49 15013 LTM -9.483115e-17
#> 50 15014 LTM -7.870370e-02
#> 51 15015 meta -1.446759e-01
#> 52 15016 RL -3.356481e-02
#> 53 15017 biased -2.118056e-01
#> 54 15019 meta -4.745370e-02
#> 55 15020 LTM -3.125000e-02
#> 56 15021 meta -2.314815e-02
#> 57 15022 meta 7.407407e-02
#> 58 15023 LTM -1.157407e-02
#> 59 28215 biased -7.870370e-02
#> 60 28241 LTM 8.680556e-02
#> 61 28242 LTM -1.967593e-02
#> 62 28243 LTM -4.166667e-02
#> 63 28284 LTM -1.504630e-01
#> 64 28303 LTM -6.712963e-02
#> 65 28306 LTM 1.041667e-02
#> 66 28307 LTM 4.861111e-02
#> 67 28308 LTM -2.546296e-02
#> 68 28309 LTM -1.099537e-01
#> 69 28325 biased -1.562500e-01
#> 70 28326 LTM -3.472222e-02
#> 71 28327 LTM -1.122685e-01
#> 72 28328 LTM -1.273148e-02
#> 73 28329 LTM -2.546296e-02
#> 74 28330 LTM 4.861111e-02
#> 75 28331 LTM -9.490741e-02
#> 76 29220 LTM -7.407407e-02
#> 77 29221 biased -2.164352e-01
#> 78 29227 LTM -1.006944e-01
#> 79 29239 meta 1.481481e-01
#> 80 29240 LTM -4.745370e-02
#> 81 29245 LTM 3.009259e-02
#> 82 29305 biased -1.817130e-01
#> 83 29318 LTM -8.564815e-02
It is difficult to assess what the model fits are capturing without examining the specific paramter sets more carefully or deducing if membership in a particular model group predicts some other cognitve or learning aspects of the subjects. First, for the cohort of subjects
These plots show group effects for uCLIMB subjects only in python and OLCTS measures and behavioral predictors.
We have 3Back and PSS for a large majority of participants - what are the group differences if any in these outcomes based on model fit?
Chantel’s request: combine language and programming measures and compare groups.
These plots show that in the biased model, most of the subjects are at very low percentage of RL use. But also, higher rates of RL use or, more even split between RL and LTM indicates a separation between s3 and s6 learning accuracy.
If that is the case, is the inclusion of the RL component a vital part of their learning make-up, however small it is? This plot shows what this group would have looked like if they relied only on LTM.
Parameter summary: what is the spread of the parameters across participants in the models?
How about some K-means clustering?
Some specific plans are to estimate the three LTM parameters for all 83 participants and see if they are related to WM, PSS measures. Also, how are the parameters related to the “separation” between s3 and s6?
Some more specific things to test might be effect of delay between stimulus presentations.